Image Preparation

Posted by Andrew Castillo on September 30, 2015

Initial notes

Our material system of interest is LLDPE which we are exploring the crystallinity. The amorphous and crystalline phases are differentiated by different scattering length densities for the respective phases.

Image Preparation

In order to perform reconstruction we need to first identify the two-point statistics of the autocorrelation in order to do phase recovery. This requires careful treatment of the data in order to successfully apply our relation from the autocorrelation to the two point statistics defined in the post here.

As a visual aid the basic process is shown below. In this plot we have $\rho(r)$ is the scattering length density distribution (SLDD) and $I(s)$ is the experimental scatter data we have. We are effectively back tracking to $\Gamma_\rho(r)$ which is the autocorrelation function of our SLDD. From here we can than find our 2-pt statistics.

Visual Aid

Raw Image

We first start with a raw image

Raw

Identify Beam Stop

Now we identify the beam stop. We are in the process of determining the best course of action to account for the beam stop. For now we will apply the max intensity to the beam stop area. It is still necessary to identify the beam stop in order to apply symmeterize the image.

Original Beam Stop

Beam Stop Raw

Corrected with Max Intensity Method

Beam Stop Corrected

Symmeterize image

Now after we have identified the beam stop we will apply symmetry to the image. Note: the image below does NOT have the corrected beam stop. Symmetry Applied

Autocorrelation

Now that we have working data we can proceed to the first step of finding the autocorrelation of the SLDD. The result is shown below.

IfftApplied

This is the first step to getting 2-pt statistics. In order to complete the conversion we relate the mean squared fluctuation of scatter length density $/eta_0^2$ and the volume fraction, $V_1$, found experimentally to $Q$, which represents the total scattering power of the specimen. This is described in detail in the post here.

Sources

[1] R. J. Roe, Methods of X-Ray and Neutron Scattering in Polymer Science, 174-176, Oxford University Press 2000.